Binomial or Geometric?

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What is a Binomial Distribution?

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A Binomial Distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. The variable can take on values from 0 to n, where n is the number of trials.

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What is a Geometric Distribution?

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A Geometric Distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials, each with the same probability of success.

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When would you use a Binomial Distribution?

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Use a Binomial Distribution when you have a fixed number of trials, each with two possible outcomes (success or failure), and you want to find the probability of a certain number of successes.

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When would you use a Geometric Distribution?

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Use a Geometric Distribution when you are interested in the number of trials until the first success occurs, with each trial being independent.

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What is the probability formula for a Binomial Distribution?

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P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

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What is the probability formula for a Geometric Distribution?

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P(X = k) = (1-p)^(k-1) * p, where k is the number of trials until the first success and p is the probability of success.

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If you flip a coin 10 times, what distribution would you use to find the probability of getting exactly 4 heads?

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Binomial Distribution.

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If you are waiting for the first customer to arrive at a store, what distribution applies?

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Geometric Distribution.

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What does 'n' represent in a Binomial Distribution?

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In a Binomial Distribution, 'n' represents the total number of trials.

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What does 'p' represent in both Binomial and Geometric Distributions?

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In both distributions, 'p' represents the probability of success on each trial.